Domain decomposition method for parabolic equation on general domain (Q1891674)

Domain decomposition procedures for parabolic problems in a rectangle have been studied by \textit{C. N. Dawson} and \textit{T. F. Dupont} [Math. Comput. 58, No. 197, 21-34 (1992; Zbl 0746.65072)]. In this paper the author considers the nonoverlapping domain decomposition method for a semilinear parabolic equation in a convex polygon in \(\mathbb{R}^2\). The method is based on a finite element procedure and different decompositions of nonoverlapping subdomains that can be implemented on parallel processors. An \(L^2\)-error estimate is given for Lipschitz continuous nonlinearities.